Berry Curvature in Graphene: A New Approach

Details Berry Curvature in Graphene: A New Approach Berry Curvature in Graphene: A New Approach

2008-02-25

arxiv.org/abs/0802.3565v3

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Slightly modified version, to appear in EPJC

Scientific paper

10.1140/epjc/s10052-008-0839-4

In the present paper we have directly computed the Berry curvature terms relevant for Graphene in the presence of an \textit{inhomogeneous} lattice distortion. We have employed the generalized Foldy Wouthuysen framework, developed by some of us \cite{ber0,ber1,ber2}. We show that a non-constant lattice distortion leads to a valley-orbit coupling which is responsible to a valley-Hall effect. This is similar to the valley-Hall effect induced by an electric field proposed in \cite{niu2} and is the analogue of the spin-Hall effect in semiconductors \cite{MURAKAMI, SINOVA}. Our general expressions for Berry curvature, for the special case of homogeneous distortion, reduce to the previously obtained results \cite{niu2}. We also discuss the Berry phase in the quantization of cyclotron motion.

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